Question

Simplify
1 ...4/9
2 ....35/111
3 .....18/13
4.......41/16
5.......101/11
6........13/17
​

Answer 1

$\star\:\:\bf\large\underline\blue{Question:-}$

• Simplify the problems.

$\star\:\:\bf\large\underline\blue{Solution:-}$

$\star\:\:\bf\underline\blue{Question\:1:-}$

$\sqrt{ \frac{80}{105} }$

$= \sqrt{ \frac{ \cancel{5 }\times 16}{ \cancel{5 }\times 81} }$

$= \sqrt{ \frac{16}{81} }$

$= \sqrt{ (\frac{4}{9})^{2} }$

$= \pm \frac{4}{9}$

$\star\:\:\bf\underline\blue{Question\:2:-}$

$\sqrt{ \frac{1225}{12321} }$

$= \sqrt{ \frac{35 \times 35}{111 \times 111} }$

$= \sqrt{( \frac{35}{111})^{2} }$

$= \pm \frac{35}{111}$

$\star\:\:\bf\underline\blue{Question\:3:-}$

$\sqrt{1 \frac{155}{169} }$

$= \sqrt{ \frac{(1 \times 155) + 169}{169} }$

$= \sqrt{ \frac{155 + 169}{169} }$

$= \sqrt{ \frac{324}{169} }$

$\sqrt{( \frac{18}{13})^{2} }$

$= \pm \frac{18}{13}$

$= \pm1 \frac{5}{18}$

$\star\:\:\bf\underline\blue{Question\:4:-}$

$\sqrt{6 \frac{145}{256} }$

$= \sqrt{ \frac{(6 \times 256) + 145}{256} }$

$= \sqrt{ \frac{1681}{256} }$

$= \sqrt{ {( \frac{41}{16}) }^{2} }$

$= \pm \frac{41}{16}$

$= \pm2 \frac{9}{16}$

$\star\:\:\bf\underline\blue{Question\:5:-}$

$\sqrt{84 \frac{37}{121} }$

$= \sqrt{ \frac{(84 \times 121) + 37}{121} }$

$= \sqrt{ \frac{10201}{121} }$

$= \sqrt{ {( \frac{101}{11}) }^{2} }$

$= \pm \frac{101}{11}$

$= \pm9 \frac{2}{11}$

$\star\:\:\bf\underline\blue{Question\:6:-}$

$\sqrt{ \frac{1183}{2023} }$

$= \sqrt{ \frac{169 \times \cancel{7}}{289 \times \cancel{ 7}} }$

$= \sqrt{ (\frac{13}{17})^{2} }$

$= \pm \frac{13}{17}$